The point group \(\mathbf {D}_{6h}\)  describes, for instance, the symmetry of the heavy-fermion material UPt\(_3\)  (Ref. UPt3-review), in which a variety of thermodynamic and transport measurements have revealed an
unconventional superconducting state. Although there is still no consensus on the pairing symmetry in UPt\(_3\) , the most promising candidate model is based on the 2D irrep \(E_{2u}\)  of \(\mathbf {D}_{6h}\) .
The corresponding order parameter is real in the high-temperature \(A\)  phase and complex (TR symmetry breaking) in the low-temperature \(B\)  phase.[1]}, [2]}, [3]}
The electron bands in UPt\(_3\)  originate from
the \(j_z=\pm 1/2\) , \(\pm 3/2\) , and \(\pm 5/2\)  doublets at the \(\Gamma \)  point, which correspond, respectively, to the \(\Gamma _7\) , \(\Gamma _9\) , and \(\Gamma _8\)  coreps of \(\mathbf {D}_{6h}\) .
